The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning including reasoning about spatial change. Finally there is a discussion of theoretical results and a glimpse of future work. The paper is a revised and condensed version of [33,34].

Qualitative Spatial Representation and Reasoning: An Overview

We propose a definition of a spatial database system as a database system that offers spatial data types in its data model and query language, and supports spatial data types in its implementation, providing at least spatial indexing and spatial join methods. Spatial database systems offer the underlying database technology for geographic information systems and other applications. We survey data modeling, querying, data structures and algorithms, and system architecture for such systems. The emphasis is on describing known technology in a coherent manner, rather than listing open problems.

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An introduction to spatial database systems

This research was partially funded by NSF grant No. IRI-9309230 and grants from Intergraph Corporation. Additional support from NSF for the NCGIA under No. SBR-9204141 is gratefully acknowledged. Max J. Egenhofer University of Maine, National Center for Geographic Information and Analysis and Department of Surveying Engineering, Department of Computer Science, University of Maine, Orono, ME 04469-5711, max@mecan1.maine.edu

Categorizing Binary Topological Relations Between Regions, Lines, and Points in Geographic Databases

This paper posits the usefulness of mental shifts of scale and perspective in thinking and communicating about spatial relations, and describes two experimental techniques for researching such cognitive activities. The first example involves mentally expanding a hand-sized piece of entangled string, a knot, so that following a portion of the string into a crossing resembles the act of walking along a path and over a bridge. The second example involves transforming experience and conceptions of the large-scale environment to small-scale representations through the act of mapmaking, and then translating the map to depictions of street-level views. When used in the context of clinical research methodologies, these techniques can help to elicit multimodal expressions of conceived topological relationships and geographical detail, with particular attention to individual differences.

Spatial Cognition II

This paper surveys the work of the qualitative spatial reasoning group at the University of Leeds. The group has developed a number of logical calculi for representing and reasoning with qualitative spatial relations over regions. We motivate the use of regions as the primary spatial entity and show how a rich language can be built up from surprisingly few primitives. This language can distinguish between convex and a variety of concave shapes and there is also an extension which handles regions with uncertain boundaries. We also present a variety of reasoning techniques, both for static and dynamic situations. A number of possible application areas are briefly mentioned.

Qualitative Spatial Representation and Reasoning with the Region Connection Calculus

Topological relationships between spatial objects represent important knowledge that users of geographic information systems expect to retrieve from a spatial database. A difficult task is to assign precise semantics to user queries involving concepts such as “crosses”, “is inside”, “is adjacent”. In this paper, we present two methods for describing topological relationships. The first method is an extension of the geometric point-set approach by taking the dimension of the intersections into account. This results in a very large number of different topological relationships for point, line, and area features. In the second method, which aims to be more suitable for humans, we propose to group all possible cases into a few meaningful topological relationships and we discuss their exclusiveness and completeness with respect to the point-set approach.

/pdf/a-small-set-of-formal-topological-relationships-suitable-for-4cggazng1c.pdf

A Small Set of Formal Topological Relationships Suitable for End-User Interaction

Qualitative representation of positional information

The 4-intersection, a model for the representation of topological relations between 2-dimensional objects with connected boundaries and connected interiors, is extended to cover topological relations between 2-dimensional objects with arbitrary holes, called regions with holes. Each region with holes is represented by its generalized region—the union of the object and its holes — and the closure of each hole. The topological relation between two regions with holes, A and B, is described by the set of all individual topological relations between (1) A ’s generalized region and B’s generalized region, (2) A ’s generalized region and each of B’s holes, (3) B’s generalized region with each of A ’s holes, and (4) each of A ’s holes with each of B’s holes. As a side product, the same formalism applies to the description of topological relations between 1-spheres. An algorithm is developed that minimizes the number of individual topological relations necessary to describe a configuration completely. This model of representing complex topological relations is suitable for a multi-level treatment of topological relations, at the least detailed level of which the relation between the generalized regions prevails. It is shown how this model applies to the assessment of consistency in multiple representations when, at a coarser level of less detail, regions are generalized by dropping holes.

Paolino Di Felice

Papers

A Small Set of Formal Topological Relationships Suitable for End-User Interaction

Qualitative representation of positional information

Topological relations between regions with holes

A comparison of methods for representing topological relationships

Approximate topological relations